APR / APY Converter
Convert between Annual Percentage Rate and Annual Percentage Yield with any compounding frequency.
Formula
Where n is the number of compounding periods per year. Daily compounding: n = 365.
The reverse formula — extracts the simple rate from a compound yield.
The theoretical limit when compounding occurs infinitely often. Used in some DeFi protocols.
Examples
- APR = 50% = 0.50, n = 365 (daily)
- APY = (1 + 0.50/365)^365 − 1
- APY = (1.001370)^365 − 1
- APY = 1.6487 − 1 = 0.6487
- APY = 100% = 1.00, n = 365 (daily)
- APR = 365 × ((1 + 1.00)^(1/365) − 1)
- APR = 365 × (2^0.002740 − 1)
- APR = 365 × 0.001899 = 0.6931
- APR = 12% = 0.12, n = 12 (monthly)
- APY = (1 + 0.12/12)^12 − 1
- APY = (1.01)^12 − 1
- APY = 1.12683 − 1 = 0.12683
Key Concepts
APR vs APY
APR (Annual Percentage Rate) is the simple interest rate without compounding. APY (Annual Percentage Yield) includes the effect of compound interest. APY is always ≥ APR. The difference grows with higher rates and more frequent compounding.
Why DeFi Uses APY
Most DeFi protocols auto-compound rewards, making APY the more accurate measure of actual returns. When a yield farm shows '200% APY,' the underlying APR is significantly lower — the high APY comes from frequent compounding.
Compounding Frequency Matters
At 50% APR: annual compounding gives 50% APY, monthly gives 63.2%, daily gives 64.9%, and continuous gives 64.9%. The difference grows dramatically at higher rates — at 1,000% APR, daily compounding yields 2,196,644% APY.
Auto-Compounding Vaults
Yield aggregators like Yearn and Beefy auto-compound your rewards, converting APR to APY automatically. They harvest rewards and reinvest them — typically daily or when gas-efficient — so you benefit from compound growth without manual claims.
Misleading APY Claims
Extremely high APY numbers (10,000%+) are often unsustainable. They assume the current rate persists for a full year with perfect compounding. In reality, DeFi yields change constantly as TVL and token prices fluctuate.
Real Yield vs Emissions
Protocol-native token emissions inflate APY but dilute token value. 'Real yield' comes from actual revenue (trading fees, interest, liquidation fees). A 10% APY from real yield is generally more sustainable than 500% APY from token emissions.
Understanding APR and APY in DeFi
APR and APY are both measures of annualized returns, but they differ in one critical way: compounding. APR is the simple rate — if you earn 1% per month, your APR is 12%. APY accounts for the fact that each month's interest earns interest in subsequent months, resulting in a higher effective return.
In DeFi, the distinction matters because most protocols compound at varying frequencies. A lending protocol might accrue interest per block (~12 seconds on Ethereum), while a yield farm might require manual harvesting and re-staking. Auto-compounding vaults bridge this gap by reinvesting automatically.
When comparing yields across protocols, always ensure you're comparing APR-to-APR or APY-to-APY. A protocol showing 50% APR with daily auto-compounding is actually yielding ~64.9% APY, which may be better than a competitor advertising 60% APY with no compounding advantage.
Frequently Asked Questions
Which should I look at — APR or APY?
If you're manually compounding or the protocol doesn't auto-compound, APR is more realistic. If the protocol auto-compounds rewards, APY reflects your actual returns. Always check whether advertised rates are APR or APY before investing.
Why does compounding frequency matter less at low rates?
At 5% APR, daily vs annual compounding only adds 0.13% (5.13% vs 5.00% APY). At 100% APR, the gap is 71.5% (171.5% vs 100.0% APY). Compounding's effect is exponential — it compounds on itself — so higher base rates amplify the difference.
What is continuous compounding?
Continuous compounding is the mathematical limit of compounding infinitely often. The formula is APY = e^APR − 1. Some DeFi protocols that accrue interest per block approximate continuous compounding. In practice, daily compounding is nearly identical to continuous.